engrjenjen
Structural
I have attached a table showing a list of allowable deflections in beam. I'm just wondering if these are applicable for any type of support condition (i.e. simply supported, fixed-end, cantilever, propped).
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Steel Beam Allowable Deflection 2
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rowingengineer
Structural
Cantilever - no
"Programming today is a race between software engineers striving to build bigger and better idiot-proof programs, and the Universe trying to produce bigger and better idiots. So far, the Universe is winning."
"Programming today is a race between software engineers striving to build bigger and better idiot-proof programs, and the Universe trying to produce bigger and better idiots. So far, the Universe is winning."
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engrjenjen
Structural
What do you typically use for cantilever?
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engrjenjen
Structural
Hi tempeng,
For the Span/180 limit, does it consider the effect of both dead and live loads? or just for the live load only? Thank you.
For the Span/180 limit, does it consider the effect of both dead and live loads? or just for the live load only? Thank you.
JasonMcKee71
Structural
Usually, cantilevers have double deflection limits compared to normally supported beams.
Jason McKee
proud R&D Manager of
Cross Section Analysis & Design
Software for the structural design of cross sections
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Jason McKee
proud R&D Manager of
Cross Section Analysis & Design
Software for the structural design of cross sections
Moment Curvature Analysis
Interaction Diagrams
Reifnorcement Design etc.
enjrjenjen said:
That's for imposed loads only. The list of limits in the standards (BS 5950 I'm assuming) are only suggestions to get you started, not "set in stone" limits. Depending on the job you want your cantilever to do, L/180 might still give an unacceptable level of deflection.
One must consider the purpose of deflection limits.
From my limited perspective, there are two primary reasons for deflection limits - the effect on finishes and the psychological effect on the occupants. If the strength requirements are met, then deflection(s) should be evaluated based on the previous considerations.
Ralph
Structures Consulting
Northeast USA
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2
- #9
Cantilevers are GENERALLY allowed twice the maximum deflection shown in your tables.
A 360" long cantilever that deflects 1" has deflected L/360. A 360" long simply supported beam that deflects 1" has deflected L/360. However, the simply supported beam deflected 1" in the center of the span and the cantilever deflected 1" at the end of the span. The simply supported beam deflected the same amount in half the distance. In terms of serviceability - vibrations and ceiling, wall, and floor finishes, the simply supported beam deflecting 1" is much 'harsher' than the cantilever because the rate of change of the slope of the beam while it is deflecting is greater.
Therefore, a 360" long cantilever deflecting 2" is equivalent to a 360" long simply supported beam deflecting 1", so where a simply supported beam is allowed to deflect L/360, a cantilever may deflect up to L/180 with the same effect.
A 360" long cantilever that deflects 1" has deflected L/360. A 360" long simply supported beam that deflects 1" has deflected L/360. However, the simply supported beam deflected 1" in the center of the span and the cantilever deflected 1" at the end of the span. The simply supported beam deflected the same amount in half the distance. In terms of serviceability - vibrations and ceiling, wall, and floor finishes, the simply supported beam deflecting 1" is much 'harsher' than the cantilever because the rate of change of the slope of the beam while it is deflecting is greater.
Therefore, a 360" long cantilever deflecting 2" is equivalent to a 360" long simply supported beam deflecting 1", so where a simply supported beam is allowed to deflect L/360, a cantilever may deflect up to L/180 with the same effect.
MikeHalloran
Mechanical
Deflection limits in buildings are generally intended to prevent a floor from feeling too 'springy', e.g. L/360, or to prevent a tile floor from cracking (where the denominator is higher than 360).
There are other reasons to worry about deflection, or to use different limits:
<old fart tale about the good old days when he was not old>
I was peripherally involved at the tail end of building an airplane flight simulator that had a beautifully elegant structure comprising bent steel pipes, split on a vertical plane and welded together around S-shaped flat plates. It worked just fine for 'heave' motion, where the simulated cockpit goes up and down.
In 'yaw' motion, where the simulated cockpit rotates around a vertical axis, the structure was much less stiff, and exhibited a structural resonance around 7 Hz, which was severe enough for the trainee pilot to detect as un-airplane-like, ruining the simulation experience. Unfortunately, the simulation required excitation in yaw in the 7 hz range, in order to faithfully recreate a buffet that originated with the real airplane's flaps. The solution, which was fairly difficult to do in those days, was to put a notch filter in the servovalve drivers so they wouldn't respond at 7 Hz, and to put some magic frequency shifting circuit ahead of that, so a 7 Hz command from the math model would actually drive the system at 6 Hz, or some frequency that was not 7 Hz.
My charter for the next generation, a simulator for helicopters, which have naturally occurring resonances up to ~25 Hz that need to be reproduced because pilots actually use them, included a new requirement that the structure have no detectable resonances, anywhere, below 100 Hz. That basically translates to ensuring that the spring rate, from anywhere to anywhere, should exceed a million pounds per inch. Again, we needed a notch filter, around 20 hz, to suppress a resonance associated with compressibility of the hydraulic fluid. The resulting structure, made of many pieces of 5x5x5/16 HSS, looked rather like the top corner of a truss bridge, but it worked per the spec.
ISTR that a L/360 structure resonates around 4 Hz, which might put the above in perspective.
</old fart tale...>
Mike Halloran
Pembroke Pines, FL, USA
There are other reasons to worry about deflection, or to use different limits:
<old fart tale about the good old days when he was not old>
I was peripherally involved at the tail end of building an airplane flight simulator that had a beautifully elegant structure comprising bent steel pipes, split on a vertical plane and welded together around S-shaped flat plates. It worked just fine for 'heave' motion, where the simulated cockpit goes up and down.
In 'yaw' motion, where the simulated cockpit rotates around a vertical axis, the structure was much less stiff, and exhibited a structural resonance around 7 Hz, which was severe enough for the trainee pilot to detect as un-airplane-like, ruining the simulation experience. Unfortunately, the simulation required excitation in yaw in the 7 hz range, in order to faithfully recreate a buffet that originated with the real airplane's flaps. The solution, which was fairly difficult to do in those days, was to put a notch filter in the servovalve drivers so they wouldn't respond at 7 Hz, and to put some magic frequency shifting circuit ahead of that, so a 7 Hz command from the math model would actually drive the system at 6 Hz, or some frequency that was not 7 Hz.
My charter for the next generation, a simulator for helicopters, which have naturally occurring resonances up to ~25 Hz that need to be reproduced because pilots actually use them, included a new requirement that the structure have no detectable resonances, anywhere, below 100 Hz. That basically translates to ensuring that the spring rate, from anywhere to anywhere, should exceed a million pounds per inch. Again, we needed a notch filter, around 20 hz, to suppress a resonance associated with compressibility of the hydraulic fluid. The resulting structure, made of many pieces of 5x5x5/16 HSS, looked rather like the top corner of a truss bridge, but it worked per the spec.
ISTR that a L/360 structure resonates around 4 Hz, which might put the above in perspective.
</old fart tale...>
Mike Halloran
Pembroke Pines, FL, USA
That's an interesting story, Mike. I wouldn't know where to begin designing something like that. I'm assuming a lot of experience was involved. Do you design each element at the interface between the simulator and the structure to be stiff enough to be above the frequencies you mentioned or is it more of a global design process where you are looking at the modal frequencies at a structure? I'm assuming it would be a mixture of both. If you only look at the global response, then localized effects caused by a flimsy member could cause vibration issues. The same would be true the other way around.
What exactly is a notch filter?
MikeHalloran said:
What exactly is a notch filter?
EdStainless
Materials
A notch filter would be the opposite of a band pass filter, it prohibits a signal in a specific frequency range.
I have seen a similar effect in the floor of a large home. No one would walk across the living room because the floor resonant freq was so near to a walking pace that it set the whole floor flexing. Having a floor move up and down 1/2" under you does not feel solid. It required a lot of stiffening to make it 'feel' right.
= = = = = = = = = = = = = = = = = = = =
P.E. Metallurgy, Plymouth Tube
I have seen a similar effect in the floor of a large home. No one would walk across the living room because the floor resonant freq was so near to a walking pace that it set the whole floor flexing. Having a floor move up and down 1/2" under you does not feel solid. It required a lot of stiffening to make it 'feel' right.
= = = = = = = = = = = = = = = = = = = =
P.E. Metallurgy, Plymouth Tube
MikeHalloran
Mechanical
The structure was triangular in plan. I modeled each side as a 2D truss.
I would have killed for a programmable calculator, but they didn't exist. We did have a monstrous Friden electro-mechanical calculator that allegedly could multiply, but nobody could remember how to make it do so.
Truss calcs involve working with very small differences between very large numbers. A slide rule doesn't have the resolution. It was all done by hand.
The most modern thing I did was steal some spreadsheet paper from the accounting department to keep the calculations organized.
Lucky for me, steel is pretty good stuff, plus when you design for high stiffness, you get low stress as a bonus. ISTR the worst case stress anywhere was something like 6 ksi.
We actually tested the structure with a dead load up to 90 Hz or so, where the 150 HP hydraulic supply ran out of steam.
The company had always been sort of low-margin, so I had to leave when my work was done, and the first 'motion platform' had been demonstrated to assemble without issues and work as it should. The company finished and installed the four units under that contract, and built another 20 or so essentially unchanged. Mine are still in service, AFAIK.
Mike Halloran
Pembroke Pines, FL, USA
I would have killed for a programmable calculator, but they didn't exist. We did have a monstrous Friden electro-mechanical calculator that allegedly could multiply, but nobody could remember how to make it do so.
Truss calcs involve working with very small differences between very large numbers. A slide rule doesn't have the resolution. It was all done by hand.
The most modern thing I did was steal some spreadsheet paper from the accounting department to keep the calculations organized.
Lucky for me, steel is pretty good stuff, plus when you design for high stiffness, you get low stress as a bonus. ISTR the worst case stress anywhere was something like 6 ksi.
We actually tested the structure with a dead load up to 90 Hz or so, where the 150 HP hydraulic supply ran out of steam.
The company had always been sort of low-margin, so I had to leave when my work was done, and the first 'motion platform' had been demonstrated to assemble without issues and work as it should. The company finished and installed the four units under that contract, and built another 20 or so essentially unchanged. Mine are still in service, AFAIK.
Mike Halloran
Pembroke Pines, FL, USA
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